Phenol release from pNIPAM hydrogels: scaling molecular dynamics simulations with dynamical density functional theory.

We employed molecular dynamic simulations (MD) and the Bennett's acceptance ratio method to compute the free energy of transfer, ΔGtrans, of phenol, methane, and 5-fluorouracil (5-FU), between bulk water and water-pNIPAM mixtures of different polymer volume fractions, ϕp. For this purpose, we first calculate the solvation free energies in both media to obtain ΔGtrans. Phenol and 5-FU (a medication used to treat cancer) attach to the pNIPAM surface so that they show negative values of ΔGtrans irrespective of temperature (above or below the lower critical solution temperature of pNIPAM, Tc). Conversely, methane switches the ΔGtrans sign when considering temperatures below (positive) and above (negative) Tc. In all cases, and contrasting with some theoretical predictions, ΔGtrans maintains a linear behavior with the pNIPAM concentration up to large polymer densities. We have also employed MD to compute the diffusion coefficient, D, of phenol in water-pNIPAM mixtures as a function of ϕp in the diluted limit. Both ΔGtrans and D as a function of ϕp are required inputs to obtain the release halftime of hollow pNIPAM microgels through Dynamic Density Functional Theory (DDFT). Our scaling strategy captures the experimental value of 2200 s for 50 µm radius microgels with no cavity, for ϕp ≃ 0.83 at 315 K.

Electrostatic depletion effects on the stability of colloidal dispersions of sepiolite and natural rubber latex.

Biocomposites based on sepiolite (Sep) clays and natural rubber latex (NRL) are novel green synthetic materials with significant mechanical performance obtained by an eco-friendly and sustainable mixing procedure, without the use of surfactants. In this work, experiments and theory are combined to investigate the stability of colloidal dispersions formed by a mixture of both negatively charged Sep fibers and non-adsorbing NRL particles. Experiments were performed by adding Sep fibers to NRL dispersions with different Sep/NRL volume fractions to evaluate the effect of Sep dispersion and NRL loading on the flocculation process. In order to theoretically understand the experimental results on colloidal stability, a density functional approach was applied to calculate the depletion interaction between two Sep fibers induced by the presence of naturally charged NRL, and an effective one-component mean-field free energy was developed to predict the phase behavior of the Sep/NRL mixture. The existence of a depletion attraction, enhanced by the electrostatic repulsion between Sep and NRL, is shown to be strong enough to induce the flocculation of the mixture at determined Sep and NRL volume fractions. The theoretical predicted phase diagram is in excellent qualitative and quantitative agreement with the experimental results, indicating that this electrostatically-enhanced depletion effect plays a key role in the colloidal stability of this system. To the best of our knowledge, this study represents the first attempt to tackle how depletion effects can be exploited to produce and control Sep/NR biocomposites.

Crossover of the effective charge in ionic thermoresponsive hydrogel particles.

We use a generalized nonlinear Poisson-Boltzmann cell model that includes excluded-volume effects to investigate whether the effective charge (Z_{eff}) of charged thermosensitive hydrogel particles increases or decreases upon the hydrogel thermal collapse. We find the existence of a crossover charge, Z^{*}, that separates two regimes. For hydrogel bare charges below Z^{*} the system shows a behavior consistent with theories based on linear approximations, i.e., Z_{eff} increases in the collapsed state. However, for bare charges above Z^{*}, the system enters an anomalous regime, in which Z_{eff} decreases in the collapsed state. We show that diluted hydrogel suspensions at low ionic strength are more likely to follow the anomalous behavior. Our theory provides a full physical justification for the controversial theoretical and experimental results reported in this regard, and describes how the interplay between electrostatic, excluded-volume and entropic effects affects this crossover.

Evidence of electrostatic-enhanced depletion attraction in the structural properties and phase behavior of binary charged colloidal suspensions.

In this paper we study the structure and phase behavior of binary mixtures of charged particles at low ionic strength. Due to the large size asymmetry between both species, light scattering measurements give us access only to the partial static structure factor that corresponds to the big particles. We observe that the addition of small charged colloids produces a decrease of the main peak of the measured static structure factor and a shift to larger scattering vector values. This finding is in agreement with theory based on integral equations with the Hypernetted-Chain Closure (HNC) relation. The effective interaction between two big particles due to the presence of small particles is obtained by a HNC inversion scheme and used in numerical simulations that adequately reproduce the experiments. We find that the presence of small particles induces an electrostatic depletion screening among the big colloids, creating around them an exclusion zone for the small charged colloids greater than that caused in the case of neutral small colloids, which in turn augments the depletion effect.

Thermoresponsive microgels at the air-water interface: the impact of the swelling state on interfacial conformation.

Poly(N-vinylcaprolactam) (PVCL) is a new temperature-responsive type of polymer microgel with improved biocompatibility as compared to more commonly used poly(N-isopropylacrylamide) (PNIPAM). Both polymers swell at low temperatures and collapse at high ones, showing a volume phase transition temperature (VPTT) around the physiological temperature. Exploring the interfacial characteristics of thermoresponsive microgels is important due to their potential application in emulsion based systems with tailored stabilities and controlled degradation profiles. In this work, we study the properties of charged PVCL particles at the air-water interface by a combination of adsorption, dilatational rheology and Langmuir monolayers. Although PVCL particles adsorb spontaneously at the air-water interface in both, swollen and collapsed conformations, the interfacial properties show significant differences depending on the swelling state. In particular, the total amount of adsorbed microgels and the rigidity of the monolayer increase as the temperature increases above the VPTT, which is connected to the more compact morphology of the microgels in this regime. Dilatational rheology data show the formation of a very loose adsorbed layer with low cohesivity. In addition, collapsed microgels yield a continuous increase of the surface pressure, whereas swollen microgels show a phase transition at intermediate compressions caused by the deformation of the loose external polymer shell of the particles. We also provide a qualitative interpretation for the surface pressure behavior in terms of microgel-microgel effective pair potentials, and correlate our experimental findings to recent rescaling models that take into account the importance of the internal polymer degrees of freedom in the rearrangement of the conformation of the microgel particles at the interface.

On the scattered light by dilute aqueous dispersions of nanogel particles.

This work deals with the scattered light by nanoparticles formed by a temperature sensitive polymer networks, namely nanogel particles. The scattered light is measured as a function of the scattering angle at temperatures below and above the volume phase transition temperature (VPTT) of nanogel particles. Our experimental results indicate that nanogel particles have a core-shell structure, formed by a uniform highly cross-linked core surrounded by a fuzzy shell where the polymer density decays to zero gradually for swollen configurations and sharply for shrunken states. The theoretical fitting of the experimental curves shows that the scattered light at low angle obeys a decreasing power law with the scattering vector, q(-α). The value of exponent α provides information about the radial dependence of the polymer density at the external shell of the particles for swollen nanogels, and about the degree of roughness of the surface for the case of shrunken nanogels. On the one hand, at low temperatures (below the VPPT), the nanogel particle is in the swollen state and the light scattering data show that its shell structure follows a fractal behaviour, with a polymer density that decays as r(α-3), where r is the distance to the particle centre. On the other hand, above the VPPT the results indicate that nanogel collapses into a core of uniform polymer density and a rough shell, with a fractal surface dimension of 2.5.

Ion permeation inside microgel particles induced by specific interactions: from charge inversion to overcharging.

In this work we have performed a theoretical study of a system formed by ionic microgels in the presence of monovalent salt with the help of Ornstein-Zernike integral equations within the hypernetted-chain (HNC) approximation. We focus in particular on analysing the role that the short-range specific interactions between the polymer fibres of the microgel and the incoming ions have on the equilibrium ion distribution inside and outside the microgel. For this purpose, a theoretical model based on the equilibrium partitioning effect is developed to determine the interaction between the microgel particle and a single ion. The results indicate that when counterions are specifically attracted to the polymer fibres of the microgel, an enhanced counterion accumulation occurs that induces the charge inversion of the microgel and a strong increase of the microgel net charge (or overcharging). In the case of coions, the specific attraction is also able to provoke the coion adsorption even though they are electrostatically repelled, and so increasing the microgel charge (true overcharging). Moreover, we show that ion adsorption onto the microgel particle is very different in swollen and shrunken states due to the competition between specific attraction and steric repulsion. In particular, ion adsorption occurs preferentially in the internal core of the particle for swollen states, whereas it is mainly concentrated in the external shell for de-swollen configurations. Finally, we observe the existence of a critical salt concentration, where the net charge of the microgels vanishes; above this inversion point the net charge of the microgels increases again, thus leading to reentrant stability of microgel suspensions.

Effective charge of ionic microgel particles in the swollen and collapsed states: the role of the steric microgel-ion repulsion.

In this work the system formed by charged (ionic) microgels in the presence of monovalent salt is investigated by solving numerically the Ornstein-Zernike integral equations within the Hypernetted-Chain approximation. The ionic density profiles, effective interaction between microgel particles, and the effective charge of the particles are calculated. In addition to the electrostatic interaction, the excluded-volume repulsion between the microgel particle and the ions is also explicitly taken into account. Although this steric interaction is irrelevant in the swollen state (when the packing fraction of the polymer network is low), it becomes a very important contribution close to the de-swollen state, hindering the counterion penetration inside the microgel mesh. The theoretical predictions indicate that the ionic density profiles are strongly affected by the degree of swelling, going from a volumetric distribution of counterions in the swollen state to a surface accumulation outside the particle that becomes more important as the particle shrinks. The electrostatic effective interaction between pairs of microgel particles is shown to be the result of a complex interplay between electrostatic and depletion effects that strongly depend on the bare charge density of the particle. For sufficiently charged microgel particles, the steric exclusion leads to a less efficient screening of the microgel charge near the de-swollen configuration, and so to a significant increase of the effective charge of the microgel particle.

Effective electrostatic interactions arising in core-shell charged microgel suspensions with added salt.

The mixture formed by charged (ionic) microgels in the presence of 1:1 added salt, with explicit consideration of a core-shell structure of the microgel particles, is studied. By solving numerically the three-component Ornstein-Zernike integral equations, the counter- and coion penetration inside the microgel network and the resulting effective microgel-microgel electrostatic interaction are calculated. This is done in the limit of very low microgel concentration, so that the resulting pair-wise effective potential is not affected by many-body particle-particle interactions. The ion-ion, microgel-ion, and microgel-microgel correlations are all treated within the Hypernetted-Chain approximation. The results obtained clearly show that the addition of salt to the microgel suspension has a deep impact on the screening of the bare charge of the particles, confirming an already well-known result: the strong reduction of the effective charge of the microgel occurring even for diluted electrolyte concentrations. We show that this effect becomes more important as we increase the shell size of the particle and derive a semi-empirical model for the effective charge as a function of the electrolyte concentration and the shell extension. The resulting microgel-microgel effective pair potential is analysed as a function of the shell extension and salt concentration. In all cases the interaction is a soft potential when particles overlap. For non-overlapping distances, our theoretical results indicate that microgel particles can be regarded as hard spherical colloids bearing an effective charge given by the net charge inside the particle and the microgel-microgel interaction shows a Yukawa-like behaviour as a function of the interparticle distance. It is also observed that increasing the bare-charge of the microgel induces a strong microgel-counterion coupling in the limit of very low electrolyte concentrations, which cannot be justified using linearized theories. This leads to an even more important adsorption of counterions inside the microgel network and to a reduction of the microgel-microgel effective repulsion.

Effective interaction in asymmetric charged binary mixtures: the non-monotonic behaviour with the colloidal charge.

In this work we study the effective force between charged spherical colloids induced by the presence of smaller charged spheres using Monte Carlo simulations. The analysis is performed for two size ratios, q = R(s)/R(b), two screened direct repulsions, κ, and two small particle packing fractions, Ø(s). We specially focus on the effect of the charge of the big colloids (Z(b)), and observe that the repulsion between big particles shows a non-monotonic behaviour: for sufficiently small charge, we find an anomalous regime where the total repulsion weakens by increasing the big colloid charge. For larger charges, the system recovers the usual behaviour and the big-big interaction becomes more repulsive increasing Z(b). This effect is linked to the existence of strong attractive depletion interactions caused by the small-big electrostatic repulsion. We have also calculated the effective force using the Ornstein-Zernike equation with the HNC closure. In general, this theory agrees with the simulation results, and is able to capture this non-monotonic behaviour.

Role of the electrostatic depletion attraction on the structure of charged liposome-polymer mixtures.

The effect of adding charged nonadsorbing polymers to electrostatically structured suspensions of charged liposomes has been experimentally studied by means of light scattering techniques. The static structure factor of the mixtures is analyzed using two polymers of different sizes. As the polymer concentration increases, the main peak of the structure factor decreases and shows an important shift to larger values of the scattering vector. Such displacement is the consequence of the electrostatic-enhanced depletion attraction induced by the polymers that counteracts the electrostatic repulsion. For the shorter polymer, the system remains stable for all studied polymer concentrations. However, for the long polymer chains, the effective attraction induced at the highest polymer density studied is strong enough to destabilize the mixture. In this case, the aggregation of the liposomes leads to clusters of nearly linear morphology. The PRISM theory is employed to calculate the effective pair potential between liposomes. The theoretical predictions are able to support the experimental observations, and provide an explanation of the interplay between the electrostatic repulsive interaction and the depletion attraction. In particular, they show that the depletion attraction is especially long ranged, and is dominated by electrostatic effects rather than entropic.

Brownian dynamics simulation of monolayer formation by deposition of colloidal particles: a kinetic study at high bulk particle concentration.

Brownian dynamics simulations (BDS) of sedimentation and irreversible adsorption of colloidal particles on a planar surface were carried out at bulk particle volume fractions (φ) in the range 0.05 to 0.25. The sedimentation and adsorption of colloidal particles were simulated as a non-sequential process that allows simultaneous settling and adsorption of particles. A kinetic model for the formation of particle monolayers based on the available surface fraction (θ(A)) is proposed to predict simulation results. The simulations show a value of 0.625 for the maximum fractional surface coverage (θ(∞)) and a monolayer structure insensitive to φ. However, the kinetic order of the monolayer formation process has a strong dependence with φ, changing from a value close to a unit, at low φ, to a value around two at high φ. This change in the kinetic reaction order is associated to differences of particle adsorption mechanism on the surface. At low φ values, the monolayer formation is achieved by independent adsorption of single particles and the reaction order is close to 1. At high φ values, the simultaneous adsorption of two particles on the surface leads to an increase of the reaction order to values close to 2.

How Péclet number affects microstructure and transient cluster aggregation in sedimenting colloidal suspensions.

We study how varying the Péclet number (Pe) affects the steady state sedimentation of colloidal particles that interact through short-ranged attractions. By employing a hybrid molecular dynamics simulation method we demonstrate that the average sedimentation velocity changes from a non-monotonic dependence on packing fraction φ at low Pe numbers, to a monotonic decrease with φ at higher Pe numbers. At low Pe number the pair correlation functions are close to their equilibrium values, but as the Pe number increases, important deviations from equilibrium forms are observed. Although the attractive forces we employ are not strong enough to form permanent clusters, they do induce transient clusters whose behaviour is also affected by Pe number. In particular, clusters are more likely to fragment and less likely to aggregate at larger Pe numbers, and the probability of finding larger clusters decreases with increasing Pe number. Interestingly, the lifetime of the clusters is more or less independent of Pe number in the range we study. Instead, the change in cluster distribution occurs because larger clusters are less likely to form with increasing Pe number. These results illustrate some of the subtleties that occur in the crossover from equilibrium like to purely non-equilibrium behaviour as the balance between convective and thermal forces changes.

Charged colloid-polymer mixtures: a study on electrostatic depletion attraction.

In this work, light scattering methods have been used to study the effect of adding charged polymer chains on the structural and dynamic properties of a charged colloidal system. The experimental measurements of the static structure factor S(cc)(q) show that as the polymer concentration increases, the main peak moves to higher q-values, which is interpreted in terms of the electrostatically enhanced depletion attraction induced by the polymer. Moreover, we found that the shift of the peak depends on the interplay between two relevant length scales, the polymer radius of gyration, R(g), and the Debye length, κ(-1). To reach these conclusions, the polymer reference interaction site model has been employed to explain the experimental results and to study how the effective depletion attraction depends on the polymer concentration, R(g) and κ(-1). Additionally, the measurements of the dynamic structure factor f(q, τ) indicate that the colloidal diffusion increases with the polymer concentration. Both static and dynamic analysis point out that the repulsion between colloids becomes weaker as the charged polymer is added.

Effects of interparticle attractions on colloidal sedimentation.

We use a mesoscopic simulation technique to study the effect of short-ranged interparticle attractions on the steady-state sedimentation of colloidal suspensions. Attractions increase the average sedimentation velocity v(s) compared to the pure hard-sphere case, and for strong enough attractions, a nonmonotonic dependence on the packing fraction phi with a maximum velocity at intermediate phi is observed. Attractions also strongly enhance hydrodynamic velocity fluctuations, which show a pronounced maximum size as a function of phi. These phenomena arise from a complex interplay between nonequilibrium hydrodynamic effects and the thermodynamics of transient cluster formation.

Electrostatic heteroaggregation regimes in colloidal suspensions.

Despite of their importance for many industrial applications and the understanding of natural phenomena, heteroaggregation processes have not been in the focus of attention of the scientific community until quite recently. Still nowadays, their tremendously complex nature turns a detailed experimental and theoretical treatment of these processes into a difficult task. Hence, we have limited the scope of this review to electrostatic heteroaggregation arising in symmetric two-component systems, i.e., those with the same concentration of cationic and anionic particles. The short and long-time aggregation kinetics will be addressed not only from an experimental but also from a theoretical and simulation point of view at almost six orders of magnitude of electrolyte concentration. The different aggregation regimes will be identified and described in detail.

Density profiles and solvation forces for a Yukawa fluid in a slit pore.

The effect of varying wall-particle and particle-particle interactions on the density profiles near a single wall and the solvation forces between two walls immersed in a fluid of particles is investigated by grand canonical Monte Carlo simulations. Attractive and repulsive particle-particle and particle-wall interactions are modeled by a versatile hard-core Yukawa form. These simulation results are compared to theoretical calculations using the hypernetted chain integral equation technique, as well as with fundamental measure density functional theory (DFT), where particle-particle interactions are either treated as a first order perturbation using the radial distribution function or else with a DFT based on the direct-correlation function. All three theoretical approaches reproduce the main trends fairly well, but exhibit inconsistent accuracy, particularly for attractive particle-particle interactions. We show that the wall-particle and particle-particle attractions can couple together to induce a nonlinear enhancement of the adsorption and a related "repulsion through attraction" effect for the effective wall-wall forces. We also investigate the phenomenon of bridging, where an attractive wall-particle interaction induces strongly attractive solvation forces.

Two-dimensional colloidal aggregation mediated by the range of repulsive interactions.

We study the effect of the interaction's range on the structural and kinetic properties of a computer-simulated two-dimensional aggregating colloidal system. For this purpose, we considered that the particles of the system interact through a repulsive Yukawa potential which depends on two parameters: the value of the interaction potential between particles in contact V0 and the range of the interaction kappa(d) . We observed that the increase of the interaction range or V0 provokes the arrangement of the small aggregates in linear structures. The repulsive interactions have also a strong influence on the kinetic behavior of the coagulation process. Indeed, they induce the formation of three different time-separated aggregation regimes. In the first regime (at early states) the aggregation is dominated by the range of the repulsive forces, and the cluster-cluster repulsion increases with the cluster size. The second regime (at intermediate times) is reached when the average cluster size is larger than the interaction range. Here, the cluster-cluster repulsions do not grow anymore with the cluster size, so the probability of overcoming the repulsive barrier is the same for all clusters. This corresponds with the so-called reaction-limited-cluster-aggregation regime, where more than one collision between the clusters is needed to form a bond. The third aggregation regime is found at long aggregation times. In this region the coagulation is mainly determined by the diffusion time and the kinetics becomes diffusion controlled. A physical interpretation for the transition between chain structures and the typical fractals aggregates from the point of view of the range of the interactions is discussed. Moreover, a method has been developed in order to obtain the effect of the interactions with a non-negligible range over the aggregation rates directly from the simulations. The relation between these different regions with the parameters of the interaction potential V0 and kappa(d) is analyzed.

Stability of binary colloids: kinetic and structural aspects of heteroaggregation processes.

This review reports on recent advances in our knowledge about the stability of binary colloids. We focus not only on experimental results but also discuss theoretical and simulation studies regarding kinetic and structural aspects of heteroaggregation processes arising in such systems. In the first part of this work, heteroaggregation of oppositely charged particles is reviewed. When the interactions are short ranged, binary diffusion-limited cluster-cluster aggregation takes place. In this case, the short time behavior of the system follows the Hogg, Healy and Fuerstenau (HHF) theory. At long times, however, stable aggregates may form and remain in the system. Furthermore, cluster discrimination is observed, clusters that differ only by one constituent particle were found to behave quite differently. When the range of the interactions is increased, the latter effects become more pronounced. The fractal dimension of heteroaggregates is, in general, smaller than the values reported for fast and slow homoaggregation processes. In some cases, even values close to unity were obtained. This means that heteroaggregates have an open branched structure that may approach a chain-like morphology. In the second part of this work, we briefly discuss similar effects arising in heteroaggregation phenomena due to differences in particle size and chemical composition. The third part of this review tackles recent developments in the field of equilibrium phase diagrams of binary colloids. In the last section, the relatively small number of papers about heteroaggregation processes in two-dimensional systems is also discussed.

Formation and structure of stable aggregates in binary diffusion-limited cluster-cluster aggregation processes.

Binary diffusion-limited cluster-cluster aggregation processes are studied as a function of the relative concentration of the two species. Both, short and long time behaviors are investigated by means of three-dimensional off-lattice Brownian Dynamics simulations. At short aggregation times, the validity of the Hogg-Healy-Fuerstenau approximation is shown. At long times, a single large cluster containing all initial particles is found to be formed when the relative concentration of the minority particles lies above a critical value. Below that value, stable aggregates remain in the system. These stable aggregates are composed by a few minority particles that are highly covered by majority ones. Our off-lattice simulations reveal a value of approximately 0.15 for the critical relative concentration. A qualitative explanation scheme for the formation and growth of the stable aggregates is developed. The simulations also explain the phenomenon of monomer discrimination that was observed recently in single cluster light scattering experiments.